Line Profile Asymmetry Measurement

ABSTRACT

This disclosure provides methods for measuring asymmetry of features, such as lines of a diffraction grating. On implementation provides a method of measuring asymmetries in microelectronic devices by directing light at an array of microelectronic features of a microelectronic device. The light illuminates a portion of the array that encompasses the entire length and width of a plurality of the microelectronic features. Light scattered back from the array is detected. One or more characteristics of the back-scattered light may be examined by examining data from the complementary angles of reflection. This can be particularly useful for arrays of small periodic structures for which standard modeling techniques would be impractically complex or take inordinate time.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/571,418, filed Dec. 28, 2006, which is a U.S. National Phaseapplication of PCT/US2004/030115, filed Sep. 13, 2004, which claims thebenefit of U.S. Provisional Application No. 60/502,444, filed Sep. 12,2003. Further, U.S. Patent Application Ser. No. 10/571,418 is acontinuation-in-part of U.S. patent application Ser. No. 10/086,339,filed Feb. 28, 2002, which claims the benefit of U.S. ProvisionalApplication No. 60/273,039, filed Mar. 2, 2001. The entirety of each ofthese applications is incorporated herein by reference.

FIELD OF THE INVENTION

1. Technical Field

The present invention relates to optical inspection of microelectronicdevices, in particular measurement of line profile asymmetry usingscatterometry.

2. Background Art

Note that the following discussion refers to a number of publications byauthor(s) and year of publication, and that due to recent publicationdates certain publications are not to be considered as prior artvis-a-vis the present invention. Discussion of such publications hereinis given for more a complete understanding and is not to be construed asan admission that such publications are prior art for patentabilitydetermination purposes.

The fabrication of a microelectronic device is a complicated procedurethat uses a variety of equipment for the different process stepsinvolved. First, the lithography process transfers the image being madeinto a light sensitive material known as photoresist. This image inphotoresist, in turn, acts as a mask for the next patterning processknown as etching. Etching is the process by which the resist image istransferred into a suitable material such as poly-silicon. Then theetched material is over-filled with some insulating materials,planarized if necessary, and the whole process begins again.

Throughout the entire process the devices being made should be symmetricin nature from step to step, i.e., a correctly manufactured transistorgate will have equal left and right sidewalls as well as other featuressuch as, but not limited to, equal left and right corner rounding. Iferrors occur during the processing, this desired symmetry may becompromised, and as a result the device integrity or functionality mayalso be compromised. If the asymmetry is quite severe the device may notfunction at all.

The present invention relates to performing symmetry/asymmetrymeasurements via scatterometry. Scatterometry is an optical inspectiontechnique well suited for the measurement of symmetry or asymmetry onmicroelectronic devices. By analyzing the light scattered from an arrayof microelectronic features, measurements of the line profile can bemade. In particular, a scatterometer that measures at complementaryangles, i.e., +45 degrees from a position perpendicular to the surfaceand −45 degrees, is ideally suited for symmetry/asymmetry measurementsbecause the reflectance properties of the line profile can vary at theseangles, although complementary angles are not necessarily needed todetect asymmetry. To enhance the sensitivity of this effect the array offeatures should be placed in a particular orientation, known throughoutthe specification and claims as a general conical configuration, namelyone in which the wave vector of the illuminating beam does not remainparallel to the array's plane of symmetry.

Prior art techniques typically employ “classic” scattering. These aremeasurements geared towards the measurement of surface roughness,defects, pitting, etc. However, the present invention is based on thephysics of diffraction, with the measurements in the invention alwaysoccurring with respect to periodic features (such as line/spacegratings).

Prior work in scatterometry used the technique for the measurement ofline profiles in resist and etched materials. C. J. Raymond, et al.,“Resist and etched line profile characterization using scatterometry,“Integrated Circuit Metrology, Inspection and Process Control XI, Proc.SPIE 3050 (1997). Embodiments of the present invention providetechniques for the measurement of asymmetric line profiles (e.g.,unequal sidewall angles).

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated into and form a partof the specification, illustrate one or more embodiments of the presentinvention and, together with the description, serve to explain theprinciples of the invention. The drawings are only for the purpose ofillustrating one or more preferred embodiments of the invention and arenot to be construed as limiting the invention. In the drawings:

FIG. 1 is a block diagram of the angular scatterometer employed in anembodiment of the present invention.

FIG. 2 illustrates the geometry of the angular scatterometry measurementemployed by an embodiment of the invention.

FIGS. 3( a) and (b) illustrate, respectively, so-called conventional andconical scatterometry measurement orientations.

FIGS. 4( a)-(c) illustrate, respectively, a symmetric and two asymmetricresist profiles.

FIG. 5 is a graph of angular signature data corresponding to theprofiles of FIGS. 4( a)-(c).

FIG. 6 is a graph of an angular scatterometry signature (mirrored) frommetal resist wafers.

FIG. 7 is a graph of sidewall angle results from wafer 5 of theresist-on-metal sample set.

FIG. 8 is a graph of an angular scatterometry signature (mirrored) froman etched poly-silicon wafer.

FIGS. 9( a) and (b) are, respectively, left and right sidewall anglecomparisons between scatterometry and cross-section SEM for the etchedpoly-silicon wafer.

FIG. 10 is a graph of an angular scatterometry signature (mirrored) froma 193 nm resist wafer.

FIGS. 11( a) and (b) are, respectively, left and right sidewall anglecomparisons between scatterometry and cross-section SEM for the 193 nmresist wafer.

FIG. 12 is a comparison of AFM and scatterometry CD measurements for the193 nm resist wafer.

FIG. 13 shows images of a grating-on-grating profile that can be usedfor measurement of overlay misalignment.

FIG. 14 is a graph of angular scatterometry signatures for the profilesof FIG. 13 employing a conventional (non-conical) scan.

FIG. 15 is a graph of (non-unique) angular scatterometry signatures forleft and right offsets employing a conventional scan.

FIG. 16 is a graph of angular scatterometry signatures for the profilesof FIG. 14 employing a conical scan.

FIG. 17 is a graph of (unique) angular scatterometry signatures for leftand right offsets employing a conical scan.

FIG. 18 illustrates an asymmetric single line model employed in theprior art, wherein the acute angles are equal to each other and theobtuse angles are equal to each other, such that the cross section ofeach line provides only two different angles;

FIG. 19 illustrates an asymmetric single line model of an embodiment ofthe invention, wherein two angles are right, angle A is obtuse and angleB is acute, such that the cross section provides three different angles;

FIG. 20 illustrates an asymmetric single line model of an embodiment ofthe invention, wherein all four internal angles differ, with angles Cand F being acute and E and D being obtuse;

FIG. 21 illustrates a line overlay asymmetric model of an embodiment ofthe invention, wherein line H is rectangular and line G is both offsetwith respect to sidewall alignment and

FIG. 22 illustrates a line overlay asymmetric model of an embodiment ofthe invention, wherein line H is rectangular and line I is offset withrespect to sidewall alignment on one side, but not on the other side,and further where the cross section of line I provides three differentangles;

FIG. 23 illustrates a line overlay asymmetric model of an embodiment ofthe invention, wherein line I is offset with respect to sidewallalignment on one side with respect to line J, but not on the other side,and further where the cross section of each of line I and J providesthree different angles;

FIG. 24 illustrates a line overlay asymmetric model of an embodiment ofthe invention, wherein line I is offset with respect to sidewallalignment on both sides with respect to line J, where the cross sectionof line I provides three different internal angles and the cross sectionof line K provides four different internal angles;

FIG. 25 is an illustration, which may be employed as a model in oneembodiment of the invention, wherein a first series of three-dimensionalposts are deposited on top of and skewed in the x and y orientationswith respect to a second series of posts, such that the posts areoff-set or contain a stair-step feature;

FIG. 26 is an illustration, which may be employed as a model in oneembodiment of the invention, wherein a first series of three-dimensionalrectilinear structures are deposited on top of and skewed in the x and yorientations with respect to a second series of rectilinear structures,such that the structures are off-set or contain a stair-step feature;

FIG. 27 is an illustration, which may be employed as a model in oneembodiment of the invention, wherein a first series of three-dimensionalrectilinear structures are deposited on top of and skewed in the x and yorientations with respect to a second series of rectilinear structures,and further wherein the cross-section of at least one of the rectilinearstructures is not rectangular and provides at least three differentinternal angles;

FIG. 28 is a graph of angular scatterometry signatures (mirrored overcomplementary ranges) of a first series of rectangular three-dimensionalrectilinear structure deposited on top of a second series of rectangularstructures structure as in FIG. 25, wherein the solid line depicts nooffset with respect to the first and second series, the dashed linedepicts a 25 nm offset, and the dotted line depicts a 50 nm offset; and

FIG. 29 is a graph of angular scatterometry signatures (mirrored overcomplementary ranges) of an oval post-on-post structure (as in FIG. 26),with a first series of three-dimensional oval-shaped posts deposited ontop of a second series of like-shaped posts, wherein the solid linedepicts no offset with respect to the first and second series, thedashed line depicts a 25 nm offset, and the dotted line depicts a 50 nmoffset.

DETAILED DESCRIPTION Overview

Aspects of the present invention provide methods and apparatus formeasuring symmetry/asymmetry of an array of microelectronic features.One embodiment of the invention provides a method of measuringthree-dimensional structure asymmetries in microelectronic devices. Inaccordance with this method, light is directed at an array ofmicroelectronic features of a microelectronic device. The lightilluminates a portion of the array that encompasses the entire lengthand width of a plurality of the microelectronic features. Lightscattered back from the array is detected at a condition selected fromthe group consisting of one or more angles of reflection, one or morewavelengths, or a combination thereof. The method also includesexamining one or more characteristics of the back-scattered light byperforming an operation comprising examining data from complementaryangles of reflection.

A method of measuring line profile asymmetries in microelectronicdevices in accordance with another embodiment of the invention involvesdirecting light at an array of microelectronic features of amicroelectronic device at an angle of incidence to the array. Lightscattered back from the array is detected at an angle complementary tothe angle of incidence. One or more characteristics of the detectedlight is compared to an asymmetric model that includes a single featureprofile that, in transverse cross-section, has an upper surface, a baseand a midline. The midline extends between the upper surface and thebase and perpendicularly to the base and the cross section isasymmetrical about the midline.

Methods of Scatterometry

By analyzing electromagnetic radiation scattered from an array ofmicroelectronic features, measurements of the line profile can be made.In some preferred embodiments, a scatterometer measures at complementaryangles, e.g., +45 degrees and −45 degrees from a position perpendicularto the surface; this has proven to be particularly well suited forsymmetry/asymmetry measurements because the reflectance properties ofthe line profile can vary at these angles. To enhance the sensitivity ofthis effect, the array of features is preferably placed in a particularorientation, known as a general conical configuration. Scatterometers inaccordance with other embodiments measure at non-complementary angles,though.

Scatterometry measurements can be performed at any complementary angles−±45 degrees is one example, but suitable pairs of complementary anglesrange from nearly 0° to nearly ±90°, e.g., about ±0.00001° to about±80°; one useful embodiment performs scatterometry measurements atcomplementary angles of about ±0.00001° to about ±47°. (One cannotmeasure reflectance at an angle complementary to a 0° angle ofincidence, so 0.00001° is arbitrarily selected here as a nominal angle;any other nominal angle may suffice.) The scatterometry measurements mayby performed at several angles or a series of angles. Furthermore,measurements at each angle may include radiation of a single wavelength(such as a laser), or may include radiation composed of severalwavelengths or broad wavelength radiation (such as a white lightsource). The intensity of the radiation alone might be measured, or theintensity and phase can be measured in tandem, similar to anellipsometry measurement.

The optimum electromagnetic radiation source will depend on the natureand size of the grating. To improve clarity, though, the followingdiscussion generally refers to the electromagnetic radiation as light.Regardless of the light source used or the manner in which it ismeasured, assuming the array is oriented in the general conicalconfiguration, comparing data from complementary angles can immediatelyshow if an asymmetry is present. Without any additional need foranalysis, if the light measurements are the same then the profile issymmetric. Conversely, if the light measurements differ then the profileis asymmetric. In general, as more complementary angles are used, thebetter the measurement sensitivity. This makes angular scatterometers(those that scan through angle) better suited than spectralscatterometers (those that scan through wavelength) for thesemeasurements of profile asymmetry. In some embodiments, thescatterometer can scan through a range of angles and a range ofwavelengths.

Applications of the complementary angle scatterometry method of theinvention include, but are not limited to:

alignment of a wafer stage with an optical system, such as that on alithography tool (stepper or scanner) or in a lithography process;

alignment of wafer with an optical system, such as that on a lithographytool (stepper or scanner) or in a lithography process;

determination of the lens aberrations present in a lithography tool orprocess;

general diagnostic of the imaging performance of a lithography tool orprocess;

measurement of the temperature uniformity of a bale process/station;

measurement of the thickness uniformity of resist spin coaters or spinprocessing;

measurement of the uniformity of a developer process/station;

characterization of an etch tool or process;

characterization of a planarization tool or process;

characterization of a metallization tool or process; and

control of any of the aforementioned processes.

In the most general sense, one goal of semiconductor processing is toproduce a device (e.g., a transistor gate) that is inherently symmetric.Indeed, it is rare that a device is produced that is intentionallynon-symmetric or asymmetric. To this end the lithography patterningprocess is geared towards symmetry, particularly with regards to footingat the bottom of a line and equivalent sidewalls. Likewise, etchprocessing also strives to produce symmetric features, in this casemostly with respect to line sidewalls. For control of either of theseprocessing steps, then, measurement techniques must be able to detectasymmetry, and preferably be able to measure any asymmetry present (suchas unequal left and right sidewalls).

Scatterometry is an optical metrology based on the analysis of lightscattered from a periodic array of features. In a strict physical sense,this light “scattered” from a periodic sample is actually due todiffraction, but in a general sense it is termed scatter here forpurposes of discussion. When a series of periodic features (known as adiffraction grating) is illuminated with a light source, the reflectanceproperties of the scattered/diffracted light depend on the structure andcomposition of the features themselves. Therefore, by analyzing thescatter “signature” one can determine the shape and dimensions of thediffraction grating.

Diffraction can actually give rise to a number of different “orders,” orlight beams, scattered from the features. In modern semiconductorproduction geometries, the period of the features is small and thereforetypically only one diffraction order exists. This order is known as the“specular” or “zeroth” order and is the light beam most frequently usedin scatterometry technology. One of the more common ways of analyzinglight scatter using the specular order is to vary the incidence angle ofthe illuminating light source (which is usually a laser). As FIG. 1illustrates, as the incident angle Θ_(i) is varied and a detector movesin tandem at angle Θ_(n) to measure the diffracted power of the specularorder, a scatter “signature” is measured. It is this scattersignature—known as an angular signature—that contains information aboutthe diffracting structure, such as the thickness of the grating and thewidth of a grating line. This angular signature, when measured properly,can also contain information about any asymmetry present in the gratinglines as well. By measuring through complementary angles (both positiveand negative with respect to normal), a signature can be obtained thatis asymmetric if the line is asymmetric. Conversely, if the line profileis in fact symmetric, the measured signature will also be symmetric.Complementary angles are not needed, however, if a suitable theoreticaldiffraction model is available for comparison purposes, and the“inverse” problem (see below) can be performed.

The scatterometry method is often described in two parts, typicallyknown as the “forward” and “inverse” problems, In the simplest sense theforward problem is the measurement of a scatter signature, and theinverse problem is the analysis of the signature in order to providemeaningful data. Many types of scatterometers have been investigatedover the years, e.g., C. J. Raymond, et al., “Metrology of subwavelengthphotoresist gratings using optical scatterometry,” Journal of VacuumScience and Technology B 13(4), pp. 1484-1495 (1995); S. Coulombe, etal., “Ellipsometric scatterometry for sub 0.1 μm measurements,”Integrated Circuit Metrology, Inspection and Process Control XII, Proc.SPIE 3332 (1999); Z. R. Hatab, et al., “Sixteen-megabit dynamic randomaccess memory trench depth characterization using two-dimensionaldiffraction analysis,” Journal of Vacuum Science and Technology B 13(2),pp. 174-182 (1995); and X. Ni, et al., “Specular spectroscopicscatterometry in DUV lithography,” Proc SPIE 3677, pp. 159-168 (1999).The most widely studied, though, have been the angular or “2-Θ.”(because of the two theta variables shown in FIG. 1) variety where, asmentioned earlier, the incident angle is varied in order to obtain ascatter signature. It is this type of scatterometer that is preferred,but not necessary, for the measurement of line profile asymmetry. Itshould be noted that the scanning optical system in FIG. 1 allows thisangular scatterometer to measure both positive and negative angles fromnormal incidence (0 degrees) Up to approximately ±47 degrees.

Several different approaches have also been explored for the solution ofthe inverse problem. C. J. Raymond, et al. (1995), supra; R. H. Krukar,Ph.D. Dissertation, University of New Mexico (1993); J. Bischoff, etal., Proc SPIE 3332, pp. 526-537 (1998); and I. J. Kallioniemi, et al.,Proc SPIE 3743, pp. 3340 (1999). Because the optical response of adiffraction grating can be rigorously simulated from Maxwell'sequations, the most common methods are model-based analyses. Thesetechniques rely on comparing the measured scatter signature tosignatures generated from a theoretical model. Both differential andintegral models have been explored. Because these diffraction models arecomputationally intensive, standard regression techniques generallycannot currently be utilized without introducing errors due to theperformance of the regression, but if the errors are small or tolerable,a regression approach could be used. Generally, however, the model isused a priori to generate a series of signatures that correspond todiscrete iterations of various grating parameters, such as its thicknessand the width of the grating lines. The set of signatures that resultswhen all parameters are iterated over some range of values is known as asignature library. When the scatter signature is measured, it iscompared against the library to find the closest match. StandardEuclidean distance measures, such as minimizing the mean square error(MSE) or root mean square error (RMSE), are used for identifying theclosest match. The parameters of the modeled signature that agrees mostclosely with the measured signature are taken to be the parameters ofthis measured signature. Scatterometers in some embodiments preferablyinclude analysis software that is based on error minimization.

In previous research scatterometry has been used for the measurement ofcritical dimensions (CDs) and profile characterization of photoresistsamples, C. J. Raymond, et al. (1995), supra; and C. Baum, et al.,“Resist line width and profile measurement using scatterometry,”SEMATECH AEC-APC Conference, Vail, Colo., (September 1999), as well asetched materials such as poly-silicon and metals, S. Bushman, et al.,“Scatterometry Measurements for Process Monitoring of Polysilicon GateEtch,” Process, Equipment, and Materials Control in Integrated CircuitManufacturing III, Proc. SPIE 3213 (1997); C. Baum, et al.,“Scatterometry for post-etch polysilicon gate metrology,” IntegratedCircuit Metrology, Inspection and Process Control XIII, Proc. SPIE 3677,pp. 148-158 (1999); and C. Raymond, et al., “Scatterometry for themeasurement of metal features,” Integrated Circuit Metrology Inspectionand Process Control XIV Proc. SPIE 3998, pp. 135-146 (2000). Because thetechnology is rapid, non-destructive and has demonstrated excellentprecision, it is an attractive alternative to other metrologies used inmainstream semiconductor manufacturing. In particular, scatterometry isquite amenable to measurements of asymmetry because, as will bedemonstrated, angular scatter “signatures” can quickly show (withoutperforming the inverse problem) if any asymmetry is present on thegrating lines.

When considering whether or not to expect symmetry in the measureddiffraction efficiency of the specular (zero order) scatter signature,it is convenient to decompose both the input and output fields into Sand P components relative to the input boundary of the grating problem(in this case the xy-plane). FIG. 2 illustrates the geometry of thesecomponents relative to the angular scan direction (scans from both thepositive and negative angular regions are shown). Note that the plane ofincidence shown in this figure is the page itself, and no reference hasyet been made with respect to the orientation of the grating relative tothis plane of incidence. From the figure we can see that there is aphase difference in the S polarization component when the beam movesfrom one half of the angular region to the other. This phase differenceis one reason why an asymmetric angular signature can be produced froman asymmetric line profile.

Grating orientation relative to the plane of incidence is anotherconsideration in the measurement of sample asymmetry. FIGS. 3A and 3Bdepict two orientations, known as the conical and conventionalconfigurations, respectively. From first principles it can be shown thata scan parallel to the grating vector (the so-called “normal” or“conventional” configuration shown in FIG. 3A) is the only case thatnever couples the S and P modes of the total electromagnetic field (see,for example, equation (48) of M. Moharam, et al., “Formulation forstable and efficient implementation of the rigorous coupled-waveanalysis of binary gratings,” J. Opt Soc. Amer. A, Vol. 12, pp.1068-1076 (May 1995)). For general conical scattering problems, if theinput illumination is in a pure P-polarization state the coupled natureof the problem tells one that one may observe both S and P components inthe output (total) field. Similarly, if the input illumination is in apure S-polarization state then we may observe both S and P components inthe output (total) field.

The scattering problem is linear and so the principle of superpositionholds. If a mixed polarization state is used for the input wave we maydecompose the input field into S and P components, solve the problemsseparately, and then superpose the resulting output fields in complexamplitude. The S component of the total output field is composed ofcontributions from both the S and P portions of the input field due tothe fully coupled nature of the problem. A similar statement is true ofthe P component of the total output field. The superposition takes placein complex amplitude and thus field components in the S-polarizationstate coming from S and P portions of the input field exhibitinterference effects. This means that relative phase differences betweenthe S and P components of the total input field can translate intoamplitude differences in the S and P components of the total outputfield. With this in mind one expects asymmetry in output diffractionefficiencies for any case where coupling is present. It should also benoted that in a strict conical scan (the wave vector of the illuminatingbeam remains parallel to the structure's plane of symmetry), a symmetricstructure produces no coupling. Hence, for this case one expectssymmetry in the measured diffraction efficiencies. Only in the case ofan asymmetric structure or a general conical scan (the wave vector ofthe illuminating beam does not remain parallel to the structure's planeof symmetry) with both S and P components present in the input beam doesone expect asymmetry in the measured S and P diffraction efficiencies.

To introduce this concept of asymmetric grating lines giving rise toasymmetric measured scatter signatures, consider the simple photoresistline profiles shown in FIGS. 4( a)-(c). FIG. 4( a) depicts a perfectlysymmetric profile with both wall angles equal to 90 degrees. In FIG. 4(b), the right wall angle has been changed to 80 degrees, while in FIG.4( c) the opposite case is illustrated (left at 80 degrees, right backto 90 degrees). FIG. 5 shows the angular scatter signatures—measuredthrough complementary angles—associated with each of these profiles. Ascan be seen in the figure, the symmetric profile yields a symmetricscatter signature for both polarizations. However, the asymmetricprofiles show a significant amount of asymmetry in both polarizations.In fact, the signatures appear to be skewed, or “tipped,” as a result ofthe profile asymmetry. Furthermore, a comparison of the signature datafor the 80/90 and 90/80 degree cases shows an interesting result—thereversal of the sidewall angles yields a reversal of the signature.Physically this reversal would be the same as rotating the wafer through180 degrees and thereby transposing the positive and negative regions ofthe scan, so this result is self-consistent. These figures alsoillustrate the advantage of angular scatterometry for determining thepresence of asymmetry since one could establish that the profiles werenon-symmetric with mere visual investigation of the signatures.

Asymmetric Model Comparison

In other embodiments, asymmetry could be determined by performing thesolution to the inverse problem, e.g., performing a model comparison,either by way of a regression or through the use of a librarycomparison. This may be advantageous if only “half-sided” (positive ornegative) angles were present, for example, or if the system was aspectral scatterometer operating at a fixed angle.

FIGS. 19 to 24 illustrate some structures in which model comparison maybe useful. Each of these drawings is a transverse cross-section of afeature, which may be referred to as a feature profile. In someembodiments, the features may be lines of a diffraction grating and thetransverse cross-section may be substantially perpendicular to alongitudinal axis (not shown) of the line. Some of the illustratedfeature profiles, e.g., FIGS. 19 and 20, are single line profiles.Others, e.g., FIGS. 21 and 22, are overlaid or multi-layer diffractionstructures that may comprise two or more features. FIG. 21, for example,may be though of as a feature profile that comprises a first single lineprofile G overlaid upon a second line profile H; in FIG. 21, anasymmetric single line profile I instead overlays the symmetric singleline profile H.

Each of the model feature profiles of FIGS. 19-24 is asymmetric. Lookingfirst at FIG. 19, the feature profile 100 includes a base 102, a top104, and left and right sidewalls 106 and 108, respectively. An idealsymmetrical may have a top 104 parallel to the base 102 that meetparallel sidewalls 106 and 108 at right angles. In FIG. 19, the leftsidewall 106 is vertical, but the right sidewall 108 slants.Consequently, the feature profile 100 is asymmetrical about a midline Zthat extends between the top 102 and the base 104 and is perpendicularto the base. In FIG. 19, the midline Z is positioned equidistant fromthe left-most point of the feature (sidewall 106) and the right-mostpoint of the feature (where sidewall 108 joins the base 102), but thereis no midline perpendicular to the base 102 about which the featureprofile 100 is symmetrical. The single line profile 110 of FIG. 21 alsoincludes a base 112, a top 114 parallel to the base, and two sidewalls116 and 118. Neither of the sidewalls 116 and 118 is vertical, but theleft sidewall 116 is slanted at one angle to vertical and the rightsidewall 118 is slanted at another angle to vertical. The featureprofile 110 therefore is asymmetrical about midline Z.

Multi-layered features may include a feature profile in one layer thatis symmetrical, such as line H in FIGS. 21 and 22, and one that isasymmetrical, such as line G in FIG. 21 and line I in FIG. 22. The lowerline profile J in FIG. 23 is not perfectly rectangular, but it issymmetrical—a midline (not shown) perpendicular to the middle of thebase of the line would yield two symmetrical halves. Despite thesymmetry of the feature profiles of one layer of the structure in FIGS.21-23, the overall feature profile is asymmetrical. In otherembodiments, the model feature profile may have two or more single-layerfeature profiles that are asymmetrical. For example, FIG. 24 illustratesa two-layered feature in which both the upper feature profile I and thelower feature profile K are asymmetrical about a vertical midline (notshown).

Many of the model feature profiles of FIGS. 19 to 24 include at leastthree different angles. As a result, the two angles on the left side ofthe profile may be right angles, but angles A and B differ from oneanother and neither is a right angle. Certain of the model figures, suchas FIG. 20 and line K of the multi-layer diffraction structure of FIG.24, have four different angles within a transverse cross-section of afeature. In FIG. 20, each of the included angles of the feature profile,i.e., angles C, D, E, and F, is different from the others. In someoverlaid or multi-layer diffraction structures, at least one, andoptionally two or more, of the overlaid features has at least threedifferent angles within a cross-section of a line.

In one embodiment of the invention, a theoretical library of single ormulti-layer diffraction structures and corresponding simulated ortheoretical diffraction signals, such as diffraction signatures, isgenerated, with theoretical diffraction signatures based on thetheoretical single or multi-layer diffraction structures compared to themeasured diffraction signature. This may be done by any number ofdifferent methods. In one approach, an actual library of theoreticaloutput signals are generated based on assigned parameters for variables.This library may be generated prior to actual measurement of adiffraction signature or may be generated in a process of matching themeasured diffraction signature to a theoretical diffraction signature.Thus, as used herein, a theoretical library includes one or both of alibrary generated independent of the measured diffraction signature anda library generated based on a theoretical “best guess” of the geometryof the measured undercut multi-layer structure and calculation of theresulting theoretical diffraction signature, with iterative comparisonto changed parameter structures to determine a best match. The librarymay optionally be pruned by removing signals that may be accuratelyrepresented via interpolation from other signals in the reference set.An index of the library can similarly be generated by correlating eachsignature with one or more indexing functions and then ordering theindex based on the magnitude of the correlation. Construction orgeneration of libraries of this type, and methods for optimizationthereof, are well known in the art.

In one approach, a rigorous, theoretical model based on Maxwell'sequations is employed to calculate a predicted optical signalcharacteristic of the diffraction structure, such as the diffractionsignature, as a function of diffraction structure parameters. In thisprocess, a set of trial values of the diffraction structure parametersis selected and a computer-representable model of the diffractionstructure, including its optical materials and geometry, is constructedbased on these values. The electromagnetic interaction between thediffraction structure and illuminating radiation is numericallysimulated to calculate a predicted diffraction-signature. Any of avariety of fitting optimization algorithms may be employed to adjust thediffraction structure parameter values, with the process iterativelyrepeated to minimize discrepancy between the measured and predicteddiffraction signature, thereby obtaining the best match. U.S. PublishedPatent Application No. US 2002/0046008 discloses one database method forstructure identification, while U.S. Published Patent Application No. US2002/0038196 discloses another method. Similarly, U.S. Published PatentApplication No. US 2002/0135783 discloses a variety of theoreticallibrary approaches, as does U.S. Published Patent Application No. US2002/0038196.

Generation of libraries from a model pattern is well known in the art,as disclosed in a number of references, such as U.S. Patent ApplicationPublication Nos. 2002/0035455, 2002/0112966, 2002/0131040, 2002/0131055and 2002/0165636, among others. Early references to these methodsinclude R. H. Krukar, S. S. H. Naqvi, J. R. McNeil, J. E. Franke, T. M.Niemczyk, and D. R. Hush, “Novel Diffraction Techniques for Metrology ofEtched Silicon Gratings,” OSA Annual Meeting Technical Digest, 1992(Optical Society of America, Washington, D.C., 1992), Vol. 23, p. 204;and R. H. Krukar, S. M. Gaspar, and J. R. McNeil, “Wafer Examination andCritical Dimension Estimation Using Scattered Light,” Machine VisionApplications in Character Recognition and Industrial Inspection, DonaldP. D'Amato, Wolf-Ekkehard Blanz, Byron E. Dom, Sargur N. Srihari,Editors, Proc SPIE, 1661, pp 323-332 (1992).

Other approaches to matching, including real-time regression analysis,may similarly be employed. These methods are known in the art, and maybe employed to determine a “best fit” theoretical diffraction signal,such as a diffraction signature, based on model permutation, such aspermutation in a single line or multi-layer diffracting structure. Inthe technique generally described as iterative regression, one or moresimulated diffraction signatures are compared to a measured diffractionsignature, thereby creating a difference of error signal, with anothersimulated diffraction signature then calculated and compared to themeasured diffraction signature. This process is repeated or iterateduntil the error is reduced, which is to say regressed, to a specifiedvalue. One method of iterative regression is non-linear regression,which may optionally be performed in a “real-time” or “on-the-fly” mode.Different iterative regression algorithms, familiar to those skilled inthe art, may be applied to interpretation of measured diffractionsignatures through comparison with simulated diffraction signaturesbased on model structure profiles.

In addition to the parameters associated with single or multi-layerpatterns as disclosed herein, other diffraction structure parametersthat may be utilized in a theoretical library include any parameter thatmay be modeled, including factors such as the period of a grating;materials parameters of the structure, including parameters of variouslayers thereof; materials parameters of the substrate on which astructure is placed, such as film thickness and index of refraction offilms underneath the structure; and various weighted or average values,such as CD at a specified location, values weighted by relativecontributions of the structure and substrates, or the like.

n yet another embodiment, short periodic structures may be modeled andthe results may be utilized, e.g., by a regression or model comparison.As used herein, the term “short periodic structures” encompassesthree-dimensional structures that have lengths short enough so that theentire length and width of two or more of the structures can beencompassed in an area illuminated by the light source of thescatterometer to be used. If the area illuminated by the intendedscatterometer is on the order of 40 μm wide, for example, the shortperiodic structures may have a longitudinal length (e.g., in a directionperpendicular to the k vector of a grating) that is less than 40 μm anda transverse spacing (e.g., the distance along the k vector of a linegrating between adjacent lines of a line grating) short enough toencompass at least two of the features. Desirably, the length of theshort periodic structures is less than one half of the width of theilluminated area so that at least two, and preferably three or more, ofthe short periodic structures may be spaced from one another yet fitlongitudinally within the illuminated area. Preferably, the length ofthe short periodic structures is short enough to become a relevantparameter with respect to the incident illumination.

In one exemplary embodiment, each of the lines of a line grating modelis defined as a series of longitudinally aligned short lines instead ofa single long line. For example, each of the short lines may be about5-20 μm long, about 0.2-1 μm wide, and about 0.5-2 μm wide. The periodbetween parallel lines may be about 0.5-2 μm. The entire length andwidth of many of the short lines of this structure would be encompassedby illumination if a scatterometer's incident radiation covered acircular area having a diameter of about 40 μm.

FIGS. 25-27 schematically illustrate short periodic structures inaccordance with select embodiments of the invention. In FIG. 25, each ofthe short periodic structures comprises an array of features, each ofwhich includes a first post or hole that overlays another post or hole.The axis (not shown) of the first post or hole in each of these featuresis offset from the axis of the second post or hole, yielding a two-layerfeature that contains a “stair-step” shape. In a preferred embodiment,the posts are oval in shape, preferably an elongated oval, therebyproviding the greatest resolution with respect to complementary angleanalysis. The array may be arranged as a series of lines of the featuresthat is periodic in the X-direction, but need not be periodic in theY-direction. In one useful model, the array is a regular array of postsor holes that have periodicity in both in the X-direction andY-direction. In FIG. 26, a first series of rectilinear features aredeposited on top of and skewed in the x and y orientations with respectto a second series of rectilinear features, such that the structures areoffset or contain a “stair-step” feature as in FIG. 25. FIG. 27 alsoincludes a first series of rectilinear features deposited on top of andskewed in the x and y orientations with respect to a second series ofrectilinear features. Unlike FIGS. 25 and 26, the transversecross-section of at least one of the rectilinear features isasymmetrical and provides at least three different internal angles. Inthe specific implementation shown in FIG. 27, both of first and secondfeatures are asymmetrical, similar to lines I and J of FIG. 23. In oneuseful embodiment, the dimensions of the structure in the horizontaldimension (with respect to the plane of the device) are different,preferably substantially different. In FIG. 26, for example, the shortlines are substantially longer (in the X-direction of FIG. 25) than theyare wide (in the Y-direction of FIG. 25). While simple circular andrectangular structures are depicted in FIGS. 25-27, methods inaccordance with other embodiments of the invention may employ anythree-dimensional structure, but preferably a repeating or periodicstructure.

Some implementations of the invention employ a theoretical model basedon the three-dimensional structure of an array of short periodicstructures. While computing a three-dimensional model is complex becauseof the large number of variables in such a structure, it is possible togenerate a model, and use this model for comparison and analysispurposes with data acquired on the actual three-dimensional structureusing scatterometry techniques discussed above. It is also possible andcontemplated that such as the three-dimensional model will utilizevarious algorithms and methodologies designed to simplify computation ofthe model.

In yet another embodiment, asymmetry in an array of three-dimensionalshort periodic features by measuring complementary angles (both positiveand negative with respect to normal), and preferably by measuringthrough a range of complementary angles Θ (again both positive andnegative with respect to normal). A signature can be obtained that isasymmetric if the three-dimensional structure is asymmetric. Conversely,if the three-dimensional structure is in fact symmetric, the measuredsignature will also be symmetric.

The utility of the invention in determining asymmetry inthree-dimensional structures by comparison of complementary angles, suchas over a range, is graphically depicted in FIGS. 28 and 29. FIG. 28 isa graph of angular scatterometry signatures (mirrored over complementaryranges) of a first series of rectangular three-dimensional rectilinearstructure deposited on top of a second series of rectangular structuresstructure as in FIG. 26. In FIG. 28, the solid line depicts no offsetwith respect to the overlaid single features, the dashed line depicts a25 nm offset of these single features, and the dotted line depicts a 50nm offset. The S-polarized measurements and the P-polarized measurementsare symmetric about the 0° angle where there is no offset (the solidline). With 25 nm offset (the dashed line) each profile (such as the SData profile or the P Data profile) is “skewed” about 0° such that eachof the S Data and P Data plots are asymmetric. As the asymmetry of thethree-dimensional structure increases, the asymmetry in the resultingplots correspondingly increases, such that the asymmetry is greater at a50 nm offset (the dotted line) than it is at a 25 nm offset (the solidline). FIG. 29 is a graph of angular scatterometry signatures (mirroredover complementary ranges) of an oval “post-on-post” three-dimensionalstructure similar to FIG. 25, wherein a first series of oval-shapedposts is deposited on top of a second series of like-shaped posts. Thesolid line in FIG. 29 depicts no offset with respect to the first andsecond series, the dashed line depicts a 25 nm offset, and the dottedline depicts a 50 nm offset. As in FIG. 28, the degree of asymmetrywithin the S Data and in the P Data correlates to the degree ofasymmetry in the three-dimensional structure.

Taking scatterometry measurements of short periodic structures atcomplementary angles in accordance with embodiments of the invention,therefore, requires comparatively very little computational power.Modeling of three-dimensional structures is intensely computational, andrigorous models of all by the simplest structures cannot readily beobtained in reasonable periods of time with current computationaldevices and programs. However, embodiments of the invention that measureat complementary angles may identify asymmetry by examining the symmetryof the collected data, which is simpler and easier from a computationalperspective.

Scatterometry is thus particularly applicable to three-dimensionalstructures-on-structures, with scatterometry measurements of the 0^(th),or specular, diffraction order sensitive to alignment shifts in thesuccessive three-dimensional structure layers. This shift in thethree-dimensional structure layer (also referred to as an offset)results in an asymmetric line profile, and that can be measured using ascatterometer in the proper measurement orientation. As is seen, thesignatures change when offsets are introduced, which is a positive signfor general measurement sensitivity. The measurement orientation can be,in one embodiment, empirically determined based on the specific natureof the most critical three-dimensional measurement (e.g., whether themost critical measurement is in the x, y or z direction). Thus inaddition to varying the angle Θ over a range (and talking measurement ofthe corresponding complementary angle in each instance), it is alsopossible to vary the angle Φ (the rotational angle), and determine theoptimal angle Φ for the three-dimensional measurement to be made.

The examples below show that scatterometry techniques in accordance withaspects of the invention have good sensitivity for measuring featureasymmetry, and can therefore be used for qualifying processes for whichsymmetric results might be desired, such as lithography and etchprocessing. Comparisons with other measurement technologies such as AFMand cross-section SEM show good consistency.

INDUSTRIAL APPLICABILITY

The invention is further illustrated by the following non-limitingexamples.

To assess the viability of performing asymmetric profile measurementsusing scatterometry three different sample types were investigated(Examples 1-3). The first sample set was comprised of three wafers ofphotoresist lines on a metal substrate. The second sample was a singlewafer of etched poly-Si. The third set was also a single wafer ofgrating lines printed in 193 nm photoresist. For each sample set the rawscatter signatures were obtained by performing measurements in a conicalscanning orientation and through positive and negative angles. Suitablescatterometry libraries were generated for each sample set and includedindependent left and right variation in sidewall as well as the otherparameters such as CD and thickness.

Example 4 illustrates the use of the invention to measure alignment oftwo successive layers on a semiconductor wafer.

EXAMPLE 1 Photoresist Lines on Metal Substrate

The line widths for this sample set were nominal 250 nm in width. Thestack composition, from the top down, was comprised of the patternedphotoresist on ARC on a TiN layer, followed by a thick AlCu layer (thiseffectively acted as the substrate).

The raw signatures from this sample set showed a good deal of asymmetry.FIG. 6 depicts one signature from this data set with the positive andnegative halves of the angular scan superimposed (“mirrored”) on top ofone another. Clearly, as the figure illustrates, the two halves are notthe same. In fact, they differ at some angles by more than 5% in termsof reflectivity, and the structure of the signature differs at someangles as well. Because the measurements were made in the conicalgrating orientation, this is a sign of profile asymmetry.

The raw signatures from this data set matched well to the model.Sidewall angle results from these wafer measurements can be seen in FIG.7. Recall that the library allowed for independent variation in the leftand right sidewall angles. In addition to the scatterometrymeasurements, AFM data from the same sites can be seen on this plot.Both the AFM and scatterometer results indicate that there is indeed adifference in the sidewall angles, and that it is in the range of 1-2degrees. The data both agree that the left wall angle is steeper thanthe right wall angle as well. The scatterometry data indicate that theleft and right angles move in tandem, i.e., that the overall width ofthe line does not change but rather “sways” by 1-2 degrees from site tosite across the wafer. This effect could be due to correlation betweenthe left and right wall angle parameters, but a check of the modeledsignature data revealed that they are quite distinct when one wall angleis left fixed and the other allowed to vary.

EXAMPLE 2

Etched poly-Si Lines

The line widths for this sample set ranged from 150 to 300 nm. The stackwas comprised of patterned (etched) poly-Si on oxide on Si substrate.The raw signatures from this sample set showed a slight amount ofasymmetry when measured in the conical configuration. FIG. 8 depicts onesuch signature with both the positive and negative halves of thesignature “mirrored” to illustrate this asymmetry.

In order to draw comparisons, the wafer used for these scatterometrymeasurements was cross-sectioned and measured by a SEM to determine thesidewall angles of the lines. FIG. 9 shows the results of comparing theleft and right sidewall angle measurements of the two technologies. Asthe figure illustrates, both tools are reporting some degree of sidewallasymmetry, with the left wall angle being generally smaller.Furthermore, the sidewall angle correlation between the two techniquesis good and shows similar trending from site to site.

EXAMPLE 3 193 nm Photoresist Lines

The last sample set investigated was a single wafer of 193 nmphotoresist lines printed on a BARC layer, a poly layer, an oxide layerand a silicon substrate. The nominal feature sizes on this wafer were180 nm lines.

For this wafer, the signature data was only mildly asymmetric whenmeasured in conical mode. FIG. 10 depicts the S and P polarizations forone of these signatures “mirrored” back upon itself. In contrast to thesignature asymmetries observed from the previous samples, this asymmetrywas relatively weak.

The left and right wall angle data for one row from this wafer can beseen in FIG. 11. Included on the plots in this figure are measurementsmade on the same sites with an AFM. Both measurement technologies agreewell in terms of the overall magnitude of the wall angles. The AFM datashows more asymmetric measurements but are generally consistent with thedata from the scatterometer. A comparison of the CD measurementsobtained by the scatterometer and AFM from this same row can be seen inFIG. 12. As this figure shows, the agreement between the AFM andscatterometer measurements is excellent. The average difference betweenthese two techniques is 2.43 nm.

EXAMPLE 4 Successive Layer Alignment Measurement

The alignment of two successive layers on a semiconductor wafer iscritical for the ultimate performance of the devices being manufactured.This alignment (also called overlay) is so important that there aretools dedicated to performing this one task. These tools are based onmeasuring images of special alignment marks printed at each layer. Asthe semiconductor industry moves towards smaller and smaller dimensions,however, there is a great deal of doubt surrounding the ability of thesetools to provide the necessary measurement resolution.

Scatterometry is a technology well-suited for overlay measurements. Byusing a grating-on-grating structure, scatterometry measurements of the0^(th), or specular, diffraction order are sensitive to alignment shiftsin the successive grating layers. This shift in the grating layer (alsoreferred to as an offset) results in an asymmetric line profile, andthat can be measured using a scatterometer in the proper measurementorientation, and preferably (though not necessarily) with the ability tomeasure complementary angles (both positive and negative angles).

FIG. 13 present images of a grating-on-grating profile that can be usedfor the measurement of overlay. Errors in aligning the two successivelayers results in a shift between the grating lines, and an asymmetricline profile. FIG. 14 present results that demonstrate sensitivity tooffsets or overlay errors for measurements performed in the conventionalorientation (see FIG. 3( a)). The signatures change when offsets areintroduced, which is a positive sign for general measurementsensitivity. However, as shown in FIG. 15, for a conventional scan thesignatures that result when same magnitude±offsets are introduced arenot unique. Hence, a conventional scan is less desirable than a conicalscan.

Repeating the exercise with conical scans results in the signaturesshown in FIGS. 16 and 17. As with conventional scans, FIG. 16 showssignature changes with offset, but FIG. 17 shows that changes are nowunique as between ±(left/right) offsets. Also note the symmetry aboutzero degrees.

Accordingly, investigation has shown that conventional and conical scansof the specular (0^(th)) order are both sensitive to offsets, but onlyconical scans provide unique signatures with respect to left/rightshifts. Existing scatterometry methods for assessing overlays involveuse of 1^(st) and higher orders and so require special measurementhardware to measure higher orders. See, e.g., Sohail Naqvi, et al.,“Diffractive techniques for lithographic process monitoring andcontrol”, JVSTB 12(6) (November 1994) (moire interferometric techniqueusing higher orders); and J. Bischoff, et al., “Light diffraction basedoverlay measurement”, Proc. SPIE Vol. 4344, pp. 222-233 (2001) (1^(st)order measurement of grating-in-grating).

The preceding examples can be repeated with similar success bysubstituting the generically or specifically described reactants and/oroperating conditions of this invention for those used in the precedingexamples.

Although the present invention is illustrated in connection withspecific embodiments for instructional purposes, the present inventionis not limited thereto. Various adaptations and modifications may bemade without departing from the scope of the invention. Therefore, thespirit and scope of the appended claims should not be limited to theforegoing description.

1. A method of measuring three-dimensional structure asymmetries inmicroelectronic devices, the method comprising: directing light at anarray of microelectronic features of a microelectronic device at aplurality of pairs of complimentary angles of incidence and a pluralityof rotational angles, wherein complimentary angles of incidence aredefined as positive and negative angles with respect to normal of themicroelectronic device and a rotational angle is defined as a plane ofincidence with respect to the orientation of the array; detecting lightscattered back from the array at the plurality of pairs of complimentaryangles of incidence and the plurality of rotational angles; anddetermining three-dimensional asymmetries in the array using thedetected light scattered back from the array.
 2. The method of claim 1wherein the plurality of rotational angles includes a conicalorientation.
 3. The method of claim 1 wherein the plurality ofrotational angles includes a non-conical orientation.
 4. The method ofclaim 1 wherein the directing step comprises directing light atsubstantially a single wavelength.
 5. The method of claim 1 wherein thedirecting step comprises directing light at a plurality of wavelengths.6. The method of claim 1, wherein directing light at the array at aplurality of complimentary angles of incidence is performed for each ofthe plurality of rotational angles.
 7. The method of claim 1, furthercomprising determining the optimal rotational angle for determining thethree-dimensional asymmetries in the array.
 8. A method of measuringline profile asymmetries in microelectronic devices, the methodcomprising the steps of: directing light at an array of microelectronicfeatures of a microelectronic device at a plurality of pairs ofcomplimentary angles of incidence and a plurality of rotational angles,wherein complimentary angles of incidence are defined as positive andnegative angles with respect to normal of the microelectronic device anda rotational angle is defined as a plane of incidence with respect tothe orientation of the array; detecting light scattered back from thearray at the plurality of pairs of complimentary angles of incidence andthe plurality of rotational angles; and comparing one or morecharacteristics of the detected light to an asymmetric model thatincludes a single feature profile that, in transverse cross-section, hasan upper surface, a base and a midline extending between the uppersurface and the base and perpendicularly to the base, wherein the crosssection is asymmetrical about the midline.
 9. The method of claim 8,wherein the transverse cross-section of the single feature profileincludes at least three different internal angles.
 10. The method ofclaim 8, wherein the transverse cross-section of the single featureprofile includes four different internal angles.
 11. The method of claim8, wherein the single feature profile is of a first line and the modelincludes a feature profile of a second line overlaid on the first line,wherein at least one of the first line and the second line comprises atleast three different internal angles on a transverse cross-section ofthe line.
 12. The method of claim 11, wherein at least one of the firstline and the second line has four different internal angles on atransverse cross-section of the line.
 13. The method of claim 11,wherein both first line and the second line comprises at least threedifferent internal angles on a transverse cross-section of each of thefirst line and the second line.
 14. The method of claim 11, where thefirst line has at least one side wall that is offset from a second sidewall of the second line.
 15. The method of claim 14, wherein the firstline has a first side wall that is aligned with a first side wall of thesecond line and a second side wall that is offset from a second sidewall of the second wall.
 16. The method of claim 8 wherein the directingstep comprises directing light at substantially a single wavelength. 17.The method of claim 8 wherein the directing step comprises directinglight at a plurality of wavelengths.
 18. The method of claim 8 whereinthe comparing step comprises comparing light intensity.
 19. The methodof claim 8 wherein the comparing step additionally comprises comparingphase.
 20. The method of claim 8 wherein the comparing step additionallycomprises comparing ratios of light magnitude and light phase.
 21. Themethod of claim 8 wherein the directing step comprises directing lightat the array of microelectronic features in general conicalconfiguration.